If the ToE does not attempt to state/prove it is the cause of intracately complex existance, then what does the ToE hang its hat on?
The theory of evolution is a model that describes the history and diversity of life on Earth, not "the cause of intricately complex existence", whatever that is.
Evolution is a theory of biology; an explanation of why life on Earth is the way it is and how it was in the past, too. It's not a model of the universe or an explanation of the meaning of existence. It's just a model that biologists use.
How does organic matter know where it needs to go to form intracately complex cells and organs, let alone intracately complex creatures that can reproduce with all the cells and organs in the right places?
That's what ID is all about, and why it's the best and most reasonable answer to life's complex existance.
I don't see how what you've just written proves that "ID is the best and most reasonable answer." Your debating tactic seems to be to assert that life is "complex", whatever that means, and then assert that that proves that ID is reasonable.
That doesn't make any sense to me. An argument that proves ID is the most reasonable explanation would, for instance, provide a measure for how to judge which theories are more reasonable than other theories, and then apply that measure to ID and evolution and show how how ID wins out. Simply asserting that ID is more reasonable than evolution merely demonstrates that you don't know how to judge what is reasonable and what is not.